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When a rubber ball bounces, it first accelerates in the positive direction (downward) then it bounces (hits the floor) .The velocity then becomes negative as the ball declerates while travelling upward - accelerates in the negative direction. After some time, the velocity is finally cancelled out by the downward force of gravity on the ball.

At this point the same amount of force pushing the ball upward is the same pushing it downward - it is at zero velocity.

My question is, how long does this period of zero velocity (motionlessness) last.

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  • $\begingroup$ Your title and actual question do not match, since in the first you are asking about weightlessness (assuming you mean no external force which will induce internal stresses), while in the other you asking about motionless (which would mean no motion/velocity which in itself is meaningless without a reference frame). $\endgroup$ – fibonatic Feb 1 '14 at 1:32
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You're confusing weightlessness with motionlessness - they are two very different things.

You feel weightless when you are in free-fall. That is, you are accelerating downward at $9.8\ \mathrm{m/s^2}$. This is always true at the very apex of the motion of an object, but it is generally true for most of the rest of its path, too. The only caveat is that air resistance will add to or subtract from your acceleration. For instance, if you fall for long enough, you will reach terminal velocity, at which point you feel like you have just as much weight as standing still on the ground, but you are supported by a blast of air rather than your legs.

Motionlessness occurs for just a single instant1 for an object thrown into the air. Because there is no air resistance if there is no motion, this is also a moment of weightlessness.

To feel (near-) weightlessness for an extended period of time while moving, I recommend going sky diving, or even riding a roller coaster with a vertical drop.


1 To address the edit: This is just a single instant, lasting for a duration of precisely $0$ in time. In the classical case of a projectile in a uniform gravitational field with no air resistance, the velocity as a function of time is $$ v(t) = v_0 - gt, $$ and there is exactly one time $t$ for which $v(t) = 0$.

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  • $\begingroup$ Thanks for the response, I think I have updated the question to reflect what I am really asking (no motion) $\endgroup$ – smac89 Feb 1 '14 at 1:49
  • $\begingroup$ I have interpreted the question as to how long it will take for the ball to bounce back after hits the ground, and it is not obvious that it reverses its motion in exactly zero seconds. This is an inelastic collision and the ball deforms during which the stress builds up that later will kick the ball back. Even if we define the ball's velocity to be the velocity of its center of mass I think the answer will be a lot more complicated than it being just a simple zero extent of instant of time. $\endgroup$ – hyportnex Feb 1 '14 at 17:19
  • $\begingroup$ I'd just like to point out, that it is most probable that in this case an instance is equivalent to the smallest amount of unit time, which (we currently believe) is the Planck time - which is the time for light to travel, in a vacuum, a distance of 1 Planck length. $\endgroup$ – Tarius Aug 13 '16 at 13:17
  • $\begingroup$ @Tarius No, the Planck time is not the smallest unit of time, nor is the Planck length the smallest unit of length. Spacetime is not discrete, and in fact this has been experimentally verified by timing photon arrival times from gamma ray bursts. It's also worth noting that the Planck mass is the mass of a single cell -- certainly there are things in the world both more and less massive than this. $\endgroup$ – user10851 Aug 13 '16 at 13:40
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This answer is in regards to your updated question:

First, there is only the force of gravity on the ball and the force of gravity is (approximately) constant. Note that the force on the ball being nonzero does not imply that the velocity must also be nonzero.

Second, the moment when the balls' velocity is zero (i.e. at maximum height before it begins falling down) is instantaneous (the ball doesn't stay at zero velocity for any length of time).

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There is nothing special about the moment you call motionless - it is motionless when looking from your frame of reference - but the ball "does not know" about that.
That means the moment is just like any other moment where it has some specific velocity v - just that v = 0 from your frame of reference.
But looking from an escalator nearby, that may be a different moment.

All the ball sees is an acceleration. We call it "Gravity of Earth" - but the ball does not know earth.
If we ignore Earth too, it gets much simpler: There is a start velocity, and an acceleration.
Whether the ball goes up, down, or is turning around all depends on from where you look.

So the moment we see the ball motionless is the instant the ball has velocity 0 relative to our frame of reference, while it is accelerated - so it does not keep this velocity, it "passes through" it.


But: Why does it look to us like the ball is motionless for a moment?

The brain is trained to recognize moving objects - we learned during evolution to react quickly to an unexpected object even at the edge of our field of view (to take care if it wants to eat us, etc).

Also, the system of eye and brain has evolved to allow us to see very fine details when nothing moves - this involves lots of processes in the brain - a lot more than just the eye itself.

The relevant point here is that these functions of the brain are different with not much in common.

When observing the ball, we watch a moving object, using one part of our brain, and when the relative velocity approaches 0, we switch to a different way of seeing, done in a different part of the brain. Then we switch back.

I assume the perceived moment of motionlessness caused by this process of switching, and specifically on the time it takes to decide when to switch back to "movement".

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